I don't think your reasoning for breaking up with her is illogical at all. It's awesome that you have such great respect and admiration for your parents. Do they know what you sacrificed? Plus, if they are going to marry you off soon, as you say, what good would it do to be in a relationship with anyone?
Now we come to the kicker: You either dive out on your own and carve your own path to happiness in this world or let Mum and Dad choose for you. Personally, no matter how much I loved my parents I could never allow them to choose a wife for me. That would be scary. I think there are bigger issues to address in your romantic world (or about to be lack thereof) than a lost girlfriend.
And if you stay in touch with her and tell her the truth you run a chance of being able to be with her in the future, provided that you aren't married, that is.
There are very few personal problems that cannot be solved with a suitable application of high explosives.